Spatial Light Modulator Using Electrowetting Cells

ABSTRACT

A spatial light modulator comprising pixels, where for each pixel, a light field amplitude transmitted by the pixel is modulated by an electrowetting cell and/or a light field phase transmitted by the pixel is modulated by an electrowetting cell.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The field of the invention is spatial light modulators, and deviceswhich contain such spatial light modulators, especially holographicdisplay devices.

2. Technical Background

Spatial light modulators (SLMs) are known from the prior art. There arevarious types of SLMs, based on various physical principles. SLMs areoptical devices that modulate an incident light field in a spatialpattern in order to reflect or to transmit an image or to generate aholographic reconstruction corresponding to an electrical or opticalinput. An SLM typically comprises a one- or two-dimensional array ofaddressable elements (pixels) which are capable of transmitting orreflecting incident light fields. Well-established examples are liquidcrystal (LC) based modulators, in which a voltage-induced birefringenceis used to modulate either the amplitude or phase of an incident lightfield. Spatial light modulators are used in almost all areas of opticaltechnologies and optical information processing which take advantage ofvariable or adaptive optical components. The applications of spatiallight modulators range from display and projection systems, tomicroscopy, beam and wave front shaping, optical metrology, masklesslithography, ultra-fast laser pulse modulation to aberration correctionin terrestrial telescopes.

Various types of SLMs are known from the prior art. These includeelectrically addressable SLMs (EASLMs), optically addressable SLMs(OASLMs) and magneto-optical SLMs (MOSLMs), for example.

SLMs may comprise an array of pixels. The term “pixel” derives from“picture element” and hence is a term associated with digital imaging.In the context of SLMs, a “pixel” is the hardware element which controlsthe display of a picture element of an image which may be seen by aviewer. The image seen by a viewer may be a holographic representationof a three-dimensional scene.

Prior art SLMs have various drawbacks. Most of the liquid-crystal-basedspatial light modulators which are commercially available today exhibitrefresh rates in a range of 60-120 Hz, which correspond to responsetimes greater than 8 milliseconds. Such switching speeds are sufficientfor many applications. However, there are many applications whichrequire a much faster switching, i.e. higher frame rates. This includesin particular applications which involve time multiplexing methods.Possible applications of time multiplexing are displays that presentdifferent information to different observers. Such displays redirect thelight to different observers and simultaneously change the informationcontent of the display designated for each observer. As long as therefresh rate per observer is more than about 60 Hz, i.e. the responsetime is below 17 ms, the observer does not perceive any flickering ofthe image displayed. Examples of possible applications are automotivedisplays, where the driver wishes to see the navigation system whereasanother passenger wishes to see a movie. Another example is 3Dautostereoscopic displays where every observer wishes to see the 3Dscene from their own perspective.

An object of the implementations disclosed in this document is tomodulate the amplitude, or the phase, or the amplitude and phase of alight field spatially, where the temporal modulation of the desiredvalues is fast compared with LC-based SLMs. The amplitude is typicallyadjustable in the entire codomain (from 0 to 1, inclusive), whereas thephase is typically adjustable in the entire codomain (from 0 to 2π,inclusive) and the target refresh rate lies within the range of betweensome hundred Hertz and some kHz, i.e. a response time of 5 millisecondsor less, but typically greater than or equal to 100 microseconds. Afurther object of the implementations is to cover the entire amplitudeand/or phase range by a relative change of the amplitude and/or phasevalues between the individual pixels of a plane one- or two dimensionalarray.

It will be appreciated by those skilled in the art that the SLMsconforming to this invention may be used in any known application inwhich SLMs are employed. While the applications of the spatial lightmodulators described here are not limited to holographic displays,holographic displays are the preferred application of the spatial lightmodulators described here. It will be appreciated by those skilled inthe art that the SLMs described herein may be used in any known form ofholographic display. However, the preferred approach of the applicant togenerating computer-generated video holograms will be described below.

Computer-generated video holograms (CGHs) are encoded in one or morespatial light modulators (SLMs); the SLMs may include electrically oroptically controllable cells. The cells modulate the amplitude and/orphase of light by encoding hologram values corresponding to avideo-hologram. The CGH may be calculated e.g. by coherent ray tracing,by simulating the interference between light reflected by the scene anda reference wave, or by Fourier or Fresnel transforms; CGH calculationmethods are described for example in US2006/055994 and in US2006/139710,which are incorporated by reference. An ideal SLM would be capable ofrepresenting arbitrary complex-valued numbers, i.e. of separatelycontrolling the amplitude and the phase of an incoming light wave.However, a typical SLM controls only one property, either amplitude orphase, with the undesirable side effect of also affecting the otherproperty. There are different ways to spatially modulate the light inamplitude or phase, e.g. electrically addressed liquid crystal SLM,optically addressed liquid crystal SLM, magneto-optical SLM, micromirror devices or acousto-optic modulators. The modulation of the lightmay be spatially continuous or composed of individually addressablecells, one-dimensionally or two-dimensionally arranged, binary,multi-level or continuous.

In the present document, the term “encoding” denotes the way in whichregions of a spatial light modulator are supplied with control values toencode a hologram so that a 3D-scene can be reconstructed from the SLM.

In contrast to purely auto-stereoscopic displays, with video hologramsan observer sees an optical reconstruction of a light wave front of athree-dimensional scene. The 3D-scene is reconstructed in a space thatstretches between the eyes of an observer and the spatial lightmodulator (SLM), or possibly even behind the SLM. The SLM can also beencoded with video holograms such that the observer sees objects of areconstructed three-dimensional scene in front of the SLM and otherobjects on or behind the SLM.

The cells of the spatial light modulator may be transmissive cells whichare passed through by light, the rays of which are capable of generatinginterference at least at a defined position and over a spatial coherencelength of a few millimetres. This allows holographic reconstruction withan adequate resolution in at least one dimension. This kind of lightwill be referred to as ‘sufficiently coherent light’. However, cellswhich operate in a reflective geometry are also possible.

In order to ensure sufficient temporal coherence, the spectrum of thelight emitted by the light source must be limited to an adequatelynarrow wavelength range, i.e. it must be near-monochromatic. Thespectral bandwidth of high-brightness LEDs is sufficiently narrow toensure temporal coherence for holographic reconstruction. Thediffraction angle at the SLM is proportional to the wavelength, whichmeans that only a monochromatic source will lead to a sharpreconstruction of object points. A broadened spectrum will lead tobroadened object points and smeared object reconstructions. The spectrumof a laser source can be regarded as monochromatic. The spectral linewidth of a LED is sufficiently narrow to facilitate goodreconstructions.

Spatial coherence relates to the lateral extent of the light source.Conventional light sources, like LEDs or Cold Cathode Fluorescent Lamps(CCFLs), can also meet these requirements if they radiate light throughan adequately narrow aperture. Light from a laser source can be regardedas emanating from a point source within diffraction limits and,depending on the modal purity, leads to a sharp reconstruction of theobject, i.e. each object point is reconstructed as a point withindiffraction limits.

Light from a spatially incoherent source is laterally extended andcauses a smearing of the reconstructed object. The amount of smearing isgiven by the broadened size of an object point reconstructed at a givenposition. In order to use a spatially incoherent source for hologramreconstruction, a trade-off has to be found between brightness andlimiting the lateral extent of the source with an aperture. The smallerthe light source, the better is its spatial coherence.

A line light source can be considered to be a point light source if seenfrom a right angle to its longitudinal extension. Light waves can thuspropagate coherently in that direction, but incoherently in all otherdirections.

In general, a hologram reconstructs a scene holographically by coherentsuperposition of waves in the horizontal and the vertical directions.Such a video hologram is called a full-parallax hologram. Thereconstructed object can be viewed with motion parallax in thehorizontal and the vertical directions, like a real object. However, alarge viewing angle requires high resolution in both the horizontal andthe vertical direction of the SLM.

Often, the requirements on the SLM are lessened by restriction to ahorizontal-parallax-only (HPO) hologram. The holographic reconstructiontakes place only in the horizontal direction, whereas there is noholographic reconstruction in the vertical direction. This results in areconstructed object with horizontal motion parallax. The perspectiveview does not change upon vertical motion. A HPO hologram requires lessresolution of the SLM in the vertical direction than a full-parallaxhologram. A vertical-parallax-only (VPO) hologram is also possible butuncommon. The holographic reconstruction occurs only in the verticaldirection and results in a reconstructed object with vertical motionparallax. There is no motion parallax in the horizontal direction. Thedifferent perspective views for the left eye and right eye have to becreated separately.

In some of the implementations described herein, electrowetting cellsare used. An early use of the term “electrowetting” was in 1981;“electrowetting” was used in G. Beni and S. Hackwood, Appl. Phys. Lett.38, 4, pp. 207-209 (1981). The electrowetting effect was originallydefined as “the change in solid electrolyte contact angle due to anapplied potential difference between the solid and the electrolyte”.Since then a number of devices based on electrowetting have beendevised. The phenomenon of electrowetting can be understood in terms ofthe forces that result from the applied electric field. The fringingfield at the corners of the electrolyte droplet tend to pull the dropletdown onto the electrode, lowering the macroscopic contact angle, andincreasing the droplet contact area. Alternatively electrowetting can beviewed from a thermodynamic perspective. Since the surface tension of aninterface is defined as the Gibbs free energy required to create acertain area of that surface, it contains both chemical and electricalcomponents. The chemical component is just the natural surface tensionof the solid/electrolyte interface with no electric field. Theelectrical component is the energy stored in the capacitor formedbetween the conductor and the electrolyte. In the present document theterm ‘electrowetting cell’ describes in particular a single opticalelement for changing the amplitude and/or phase of a wave field. Theelectrowetting cell includes a chamber having cell walls filled with atleast two different non-miscible fluids or liquids, especially aconductive polar fluid or liquid, like water, and an insulatingnon-conductive fluid or liquid, like oil. It is noted and understoodthat a fluid can be a liquid or a gas. In general, a fluid is a subsetof the phases of matter and include liquid, (saturated) gas, plasma and,to some extent, plastic solid. It is noted that the term“electrowetting” within the context of this document is also to beunderstood as “electrowetting-on-dielectrics” (EWOD).

3. Discussion of Related Art

WO 2004/044659 (US2006/0055994) filed by the applicant describes adevice for reconstructing three-dimensional scenes by way of diffractionof sufficiently coherent light; the device includes a point light sourceor line light source, a lens for focusing the light and a spatial lightmodulator. In contrast to conventional holographic displays, the SLM intransmission mode reconstructs a 3D-scene in at least one ‘virtualobserver window’ (see Appendix I and II for a discussion of this termand the related technology). Each virtual observer window is situatednear the observer's eyes and is restricted in size so that the virtualobserver windows are situated in a single diffraction order, so thateach eye sees the complete reconstruction of the three-dimensional scenein a frustum-shaped reconstruction space, which stretches between theSLM surface and the virtual observer window. To allow a holographicreconstruction free of disturbance, the virtual observer window sizemust not exceed the periodicity interval of one diffraction order of thereconstruction. However, it must be at least large enough to enable aviewer to see the entire reconstruction of the 3D-scene through thewindow(s). The other eye can see through the same virtual observerwindow, or is assigned a second virtual observer window, which isaccordingly created by a second light source. Here, a visibility regioni.e. the range of positions from which an observer can see a correctreconstruction, which would be rather large, is limited to the locallypositioned virtual observer windows. This virtual observer windowsolution uses the larger area and high resolution of a conventional SLMsurface to generate a reconstruction which is viewed from a smaller areawhich is the size of the virtual observer windows. This leads to theeffect that the diffraction angles, which are small due to geometricalreasons, and the resolution of current generation SLMs, are sufficientto achieve a high-quality real-time holographic reconstruction usingreasonable, consumer level computing equipment. A mobile phone whichgenerates a three dimensional image is disclosed in US2004/0223049.However, the three dimensional image disclosed in US2004/0223049 isgenerated using autostereoscopy. One problem with autostereoscopicallygenerated three dimensional images is that typically the viewerperceives the image to be inside the display, whereas the viewer's eyestend to focus on the surface of the display. This disparity betweenwhere the viewer's eyes focus and the perceived position of the threedimensional image leads to viewer discomfort after some time in manycases. This problem does not occur, or is significantly reduced, in thecase of three dimensional images generated by holography.

SUMMARY OF THE INVENTION

According to the invention, a spatial light modulator comprising pixels,where for each pixel, a light field amplitude transmitted by the pixelis modulated by an electrowetting cell and/or a light field phasetransmitted by the pixel is modulated by an electrowetting cell.

In a preferred embodiment of the spatial light modulator especially formodulating the light field amplitude, each electrowetting cell comprisesa first substantially transparent substrate coated with a substantiallytransparent electrode and a hydrophobic isolation layer, apixel-separating side wall, at least two immiscible liquids, one of theliquids being opaque or absorbing and one of the liquids beingelectrically conductive or polar liquid, and a second, substantiallytransparent substrate and where the amount of light passing through theelectrowetting cell is controlled by a voltage applied to theelectrically conductive or polar liquid. Even though it is mentionedthat the electrowetting cell comprises at least two immiscible liquids,in general instead of a liquid of the electrowetting cell, immisciblefluids could be used.

Preferably each electrowetting cell comprises a first substantiallytransparent substrate coated with a substantially transparent electrodeand hydrophobic isolation layers, a pixel-separating side wall, a firstopaque or absorbing liquid and a second electrically conductive or polarliquid where these two liquids are immiscible, and a second,substantially transparent substrate and where the amount of lightpassing through the electrowetting cell is controlled by a voltageapplied to the electrically conductive or polar liquid.

A contact angle of the electrically conductive or polar liquid and thefirst substantially transparent substrate could be continuously variableby applying different voltages thus realising a continuously variableabsorption in the cell.

The top face of the second substrate could be coated with an opticallynon-transparent, layer, which exhibits an essentially centrally disposedoptically transmitting opening.

Preferably, the electrowetting cell is in the ON state if a DC or ACvoltage is applied between an electrode and a counter electrode, wherebythe electrically conductive or polar liquid is attracted to thehydrophobic insulator layer caused by electrostatic forces, therebydisplacing the opaque or absorbing liquid, which is positioned around acentral spot on the first substantially transparent substrate, and thecell is in its OFF state if no voltage is applied.

In one embodiment, the opaque or absorbing liquid could be disposed atfringes of the electrowetting cell and is held in this position bysuitable means such that if no voltage is applied, the opaque orabsorbing liquid spreads across the base area; a small separation ringis positioned in the centre of the cell, which ensures that there ispermanent contact to the electrically conductive or polar liquid andthat the opaque or absorbing liquid spreads homogeneously in alldirections when the cell is switched on.

In a preferred embodiment of the spatial light modulator especially formodulating the light field phase, each electrowetting cell comprises atleast three non-mixable liquid layers with at least two variablyadjustable optical interfaces, where at least two liquids exhibitdifferent optical properties. The liquid layer in the middle of thethree liquid layers could form an inclined, essentially plane platewhich is operated in a higher order for phase modulation.

The liquid layer in the middle of the three liquid layers could form aninclined, essentially plane plate, and a second electrowetting cell isplaced after the first cell to compensate for lateral offset of lightbeams transmitting the first electrowetting cell if necessary.

The liquid layer in the middle of the three liquid layers could form aninclined, essentially plane plate, and a fixed prism is placed on a beamexit side of the electrowetting cell to compensate for lateral offset oflight beams transmitting the electrowetting cell if necessary.

The liquid layer in the middle of the three liquid layers could form aninclined, essentially plane plate, and a fixed prism is placed on thebeam entrance side of the electrowetting cell to compensate for lateraloffset of light beams transmitting the electrowetting cell if necessary.

The liquid layer in the middle of the three liquid layers could form aninclined plane plate, and an aperture is disposed in a central positionon a beam exit side of the electrowetting cell to prevent lateral offsetof light beams transmitting the electrowetting cell if necessary.

In another embodiment of the invention, for each pixel, the light fieldis modulated on a complex number basis using two electrowetting cells inseries for each pixel, the two electrowetting cells permittingindependent modulation of amplitude and phase of the complex number. Thetwo cells could be located in sufficient proximity that cross-talkbetween pixels is zero or is kept to acceptable levels.

Multiple pixels could be arranged in the form of a line array or matrix.

The light field amplitude transmitted by each pixel could be modulatedwith a switching time less than or equal to 5 ms and/or greater than orequal to 100 microseconds. The spatial light modulator could be operableat conventional switching frequencies, preferably in the frequency rangefrom 15 Hz to several KHz. Alternatively or additionally, the spatiallight modulator could be operable to maintain a predetermined state fora predetermined period of time.

The electrowetting cell could be positioned near a focus of a focusingelement. The size of the electrowetting cell could be smaller or muchsmaller than the size of the focusing element.

The light transmitted through the electrowetting cell could betransmitted with a spherical or cylindrical outgoing wavefront, due toat least one light beam forming means being assigned to theelectrowetting cell.

The modulated light could be visible light and/or near infra red lightand/or near ultraviolet light. The spatial light modulator could be usedin military applications, especially in laser radar systems. The spatiallight modulator could be used to form a secondary light source. Thespatial light modulator could be used to form a light source array withvariable amplitude. Alternatively, the spatial light modulator could beused to form a light source array with variable phase. The spatial lightmodulator could be used in transmission or in a reflective geometry.

The spatial light modulator could be used in a 3D display. The spatiallight modulator could be used in a holographic display or in astereoscopic display or in an auto stereoscopic display. One or twovirtual observer windows for the eyes of one or more observers could beused.

The spatial light modulator could be used in a two dimensional amplitudemodulating display.

According to an aspect of the invention, a device includes the spatiallight modulator of any of the Claims 1 to 31, in which the device is aphase and/or an amplitude modulating device or in which the device is acomplex light wave modulating device.

According to another aspect of the invention, a display device includesthe spatial light modulator of any of Claims 1 to 31. The display devicecould have up to several million pixels. The display device couldcontain a diffuser foil.

The display device could be a 2D phase modulating display device or astereoscopic display device. Alternatively, the display device could bea holographic display device. The holographic display device preferablyuses virtual observer windows for the eyes of the observer or observers.

According to still another aspect of the invention, a method uses adisplay device of any of Claims 33 to 37, the display including a lightsource and an optical system to illuminate the spatial light modulator;the method comprising the step of:

for each pixel, modulating the light field amplitude phase transmittedby each pixel using an electrowetting cell and/or modulating the lightfield phase transmitted by each pixel using an electrowetting cell.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of one electrowetting cellwith a central absorbing oil droplet, where sub-figure (a) shows thecell in its ON state, sub-figure (b) shows the cell in its OFF state,and sub-figure (c) shows the cell in a partially light-attenuatingstate.

FIG. 2: FIGS. 2A and 2B are cross-sectional views of one display pixel,comprising the electrowetting cell positioned near the focus of a firstfocusing element and a second, confocally positioned focusing element.

FIG. 3: FIGS. 3A and 3B are cross-sectional views of one display pixel,comprising the electrowetting cell positioned near the focus of afocusing element which is followed by a diffuser foil.

FIG. 4: FIGS. 4A and 4B show the combination of a spherical focusingelement with an electrowetting cell comprising a circular pinholeaperture and an alternative combination of a cylindrical focusingelement with an electrowetting cell comprising a slit aperture,respectively.

FIG. 5: FIGS. 5A and 5B show a schematic cross-sectional view of oneelectrowetting cell with a ring-shaped absorbing oil droplet, with thecell in its ON state and the cell in its OFF state, respectively.

FIG. 6 shows how a controllable refractive index n_(LC) of a liquidcrystal inside a surface relief grating leads to a controllableintensity of a fixed focal point. The part of the diffracted light(dashed line) depends on the diffraction efficiency η of the diffractivestructure. The diffraction efficiency is changed by the change of themodulation Δn(∪)=n_(LC)(∪)−n_(substrate).

FIG. 7 shows different arrangements of a combination of a surface reliefgrating and a liquid crystal to realize an amplitude modulation.

FIG. 8 shows how a circular focus can be used to obtain an amplitudemodulating device with a high contrast. By changing the focal length ofa lens the intensity value being transmitted can be chosen. A circularspot is realized by a combination of an axicon and a lens. Also acircular phase function in front of a lens can be used to obtain acircular focus. An enlarged circular focus will be stopped by theaperture stop AS in a way that no light will pass the central clear areaof the aperture stop AS. Thus a high contrast can be obtained.

FIG. 9 shows a setup of a lens and an axicon which is placed behind thelens.

FIG. 10 shows a side view of a combination of a lens and an axicon whichforms a circular focus.

FIG. 11 shows a circular focus behind a combination of a lens and anaxicon.

FIG. 12 shows a side view and beam path through a combination of a lensand an axicon which forms a circular focus. The diameter of the circularfocus can be changed continuously by changing the focal length of thelens.

FIG. 13 shows generating a circular focus by combining a lens with anaxicon in a single element.

FIG. 14 shows a realized circular focus in the image plane of the setupshown in FIG. 13.

FIG. 15 shows a realized focus in the image plane of the setup shown inFIG. 13 in the case of an increased focal length f. Compared to FIG. 14,the focal length is enlarged by thirty percent in this example.

FIG. 16 shows an optical phase modulating element, using anelectrowetting cell.

FIG. 17 shows an optical phase modulating element, using anelectrowetting cell.

FIG. 18 shows an optical phase modulating element, using anelectrowetting cell.

FIG. 19 shows an optical phase modulating element, using anelectrowetting cell, with a prism for altering the beam propagationdirection.

FIG. 20 shows an optical phase modulating element, using anelectrowetting cell, with an aperture on the side from which the beamexits.

FIGS. 21A, B and C show the lateral beam offset or lateral shift of thebeam, the optical path length difference and the phase lag,respectively, as a function of the inclination angle γ, calculated forthe example shown in FIG. 16.

FIG. 22 shows an optical arrangement of a preferred embodiment of thepresent invention, wherein amplitude and phase modulation issequentially applied.

FIG. 23 shows a part of an optical arrangement of a preferred embodimentof the present invention, wherein a light source array can be provided,the single light sources of the light source array comprisevariable/adjustable phase values.

FIG. 24 shows a part of another optical arrangement of a preferredembodiment of the present invention, wherein a light source array can beprovided, the single light sources of the light source array comprisevariable/adjustable phase and amplitude values.

DETAILED DESCRIPTION

Various Implementations will now be described.

A. Spatial Light Modulator for Modulating Light Field Amplitude andDisplay Device Using Electrowetting Cells

This implementation relates to a spatial light modulator, and inparticular to a spatial light modulator comprising pixels, where foreach pixel, a light field amplitude transmitted by the pixel ismodulated by an electrowetting cell. The spatial light modulator may beused to generate a desired video hologram.

This implementation relates to a spatial light modulator, and inparticular to a spatial light modulator suitable for displaying dynamiccomputer-generated holograms, where the amplitude of a light field isspatially modulated. It also relates to an active matrix display deviceincorporating a spatial light modulator according to the implementation,more particularly to an electrowetting display device. It furtherrelates to a switchable light source and light source array with anindividually adjustable intensity incorporating a light modulator of thepresent implementation.

It is an object of the present implementation to provide a fast or veryfast amplitude modulation of a light field using the electrowettingprinciple, and a corresponding display device. However, the spatiallight modulator may also be operable at more conventional switchingfrequencies.

Each electrowetting cell comprises at least a first substantiallytransparent substrate coated with a substantially transparent electrodeand hydrophobic isolation layers, a pixel-separating side wall, a firstopaque or absorbing liquid and a second electrically conductive or polarliquid where these two liquids are immiscible, and a second,substantially transparent substrate. The amount of light passing throughthe electrowetting cell is controlled by a voltage applied to theelectrically conductive or polar liquid.

According to a first implementation, a spatial light modulator isprovided having a plurality of electrowetting cells. In a preferredexample, each cell comprises the following:

-   -   A first, substantially transparent substrate coated with a        substantially transparent electrode and hydrophobic isolation        layers;    -   A pixel-separating side wall    -   A first, opaque or light absorbing liquid and a second,        electrically conductive or polar liquid where those two liquids        are non-mixable;    -   A second, substantially transparent substrate optionally coated        with a substantially light absorbing layer with a centrally        disposed transparent aperture,

where the electrowetting cell is positioned near the focus of a focusingelement, and where the amount of light passing through theelectrowetting cell is controlled by a voltage applied to the secondliquid such that the contact angle of said first opaque liquid ischanged, and therefore the shape of the interface between saidimmiscible liquids is modified, and as a consequence, more or less lightis absorbed by the opaque liquid. The electrowetting cell is smaller ormuch smaller than the focusing element. The applied voltage is applieddirectly such as from a controllable source of electrical potentialdifference, such as in an electrically addressable SLM. The contactangle of the electrically conductive or polar liquid and the firstsubstantially transparent substrate is continuously variable by applyingdifferent voltages thus realising a continuously variable absorption inthe cell.

A display device according to the present implementation comprises alight source, a first focusing element, said electrowetting cell, and asecond focusing element. The minimum pixel pitch of the display isdefined by the size of the light focusing element.

According to a second implementation, a switchable point source or pointsource array having one or more electrowetting cells is provided. Aswitchable point source or point source array according to the presentimplementation comprises a light source, a focusing element, and saidelectrowetting cell.

The terms ‘opaque’, ‘absorbing’ and ‘transparent’ denotewavelength-dependent material properties, i.e. they are related to thewavelength of the electromagnetic radiation whose amplitude is to bemodulated with the help of the modulator according to thisimplementation. The modulator according to this implementation is thusnot limited to the spectral range of the visible light, but includes thenear infra red and near ultraviolet. For example, military applicationsin the near infra red are possible, such as in laser radar systems.

The implementation will now be described in detail with the help ofparticular examples. The examples relate to the electrowetting approachand can be combined with various focusing elements to realize amplitudemodulating spatial light modulators. These spatial light modulators canbe used in display devices, especially in holographic display devices.It is also possible to use these spatial light modulators to form asecondary light source or a light source array with variable amplitude.Secondary light sources may be used in back light units (BLU) of displaydevices.

FIG. 1 illustrates a first example of an electrowetting cell. Itcomprises a hermetically sealed hollow body which is filled with twoimmiscible liquids. One of the liquids is optically transparent, polarand electrically conductive; it will be referred to below as awater-based liquid. It is known from the prior art that this liquid canbe water with added salts, or a polar or conductive liquid, or any otherliquid which is made conductive by adding ionic components. A secondliquid comprises an optically opaque, light absorbing liquid, e.g. anoil-based liquid. This second liquid is electrically insulating ornon-polar; suitable substances are for example oils, alkanes or alkanemixtures. It is known that both liquids preferably have the same orsimilar density, so as to prevent shape deviations due to gravitationalforce or mechanical vibrations.

The shape of the light absorbing liquid can be changed in a specificmanner taking advantage of the electrowetting principle such that thetransmitted optical radiation is not attenuated, or is partly or fullyattenuated. The electrowetting cell according to this implementationcomprises a transparent substrate (e.g. glass or plastic) on to which athin electrode film (e.g. an indium-tin oxide (ITO) layer, approx.50-100 nm thick) is applied which is optically transparent andelectrically conductive. The ITO coating can be applied for example withthe help of sputtering processes. Then, for example, an approx. 1 μmthick, hydrophobic dielectric insulator layer is applied on to theelectrode film, such as by way of clip coating and curing. Thisinsulator film can for example be made using an amorphous fluoro-polymer(e.g. Teflon) dissolved in a fluoride solution. An additional centringmeans may be disposed in the centre of the cell, for example ahydrophobic spot, which enables the oil-based liquid droplet to be heldin a preferred position. The side walls of the cell can be made byshaping silicon, e.g. with the help of commonly used etching processes,such as reactive ion etching (RIE) or plasma etching (ICP).Alternatively, optical structuring methods can be used, and the sidewalls can be formed using photoresist. In the case silicon walls areused, these directly form the counter electrode; if photoresist wallsare used, these may be additionally coated with a conductive material orthe electrical supply line ends directly in the water-based liquidvolume. A further thin cover substrate seals the cell hermetically.

According to a preferred example of the electrowetting cell, the topface of the cover substrate is coated with an optically non-transparent,preferably absorbing layer, which exhibits a centrally disposedoptically transmitting opening (pinhole aperture). This aperture effectsa spatial filtering and represents a secondary light source withadjustable intensity. In this implementation, the light is transmittedthrough the electrowetting cell with a spherical or cylindrical outgoingwavefront, where the cell is positioned near a focal point or near thebeam waist of a ray bundle or of a Gaussian beam. The cell is in the ONstate if a DC or AC voltage is applied between electrode and counterelectrode, as shown in FIG. 1( a). In this state, the electricallyconductive or polar liquid or water-based liquid is attracted to thehydrophobic insulator layer caused by electrostatic forces, therebydisplacing the opaque or absorbing or oil-based droplet, which ispositioned around the central spot. As a consequence, a large portion ofthe light is transmitted through the cell. By applying differentvoltages, the water contact angle can be varied continuously, thusrealising a continuously variable absorption in the cell, resulting inan amplitude A of the light passing through the electrowetting cell, asshown in FIG. 1( c). The cell is in its OFF state if no voltage isapplied, as shown in FIG. 1( b). Due to the hydrophobic coating of thedielectric base substrate, the oil droplet spreads across the entirebase area or at least across large parts of it. The light which isincident on the cell is fully absorbed in the OFF state.

FIG. 5 illustrates a second example of an electrowetting cell. Incontrast to the first example in FIG. 1, the opaque or absorbing liquidor oil-based liquid is disposed at the fringes of the electrowettingcell and is held in this preferred position by suitable means. If novoltage is applied, the oil-based liquid spreads across the base area. Asmall separation ring can preferably be positioned in the centre of thecell, which ensures that there is permanent contact to the water-basedsolution and that the oil spreads homogeneously in all directions whenthe cell is switched on. Other examples of electrowetting cellconfigurations will be obvious to those skilled in the art.

FIG. 2 shows the use of an electrowetting cell in combination with twoconverging or focusing elements according to a first example of adisplay device. The combination of these three elements represents apixel of a display. The minimum pixel pitch is determined by the size ofthe focusing element. The electrowetting (EW) cell may be small or verysmall compared with the lateral dimension of a focusing element, whichallows very fast switching times to be achieved, because the liquidvolume to be moved is small, and the distance to be moved is small. Atypical switching time is in the range from 100 microseconds to 5milliseconds, but it strongly depends on the cell size. The cell isdisposed near the focal point of the first focusing element or near theintermediate image of a light source. The position is preferably chosensuch that the exit pupil of the electrowetting cell coincides with theposition of the intermediate focus. The axial shift of the intermediatefocus due to refraction at the electrowetting cell is preferably takeninto account. The exit pupil of the electrowetting cell represents asecondary light source, which is imaged through a second optical elementinto the desired position. FIG. 2 shows a refractive microlens whichcollimates the light again. Alternatively, the second optical elementcould have a diverging effect or be disposed non-confocally to theintermediate focus. The effect of the optical elements shown can berefractive, but also reflective or diffractive. The two sub-figures ofFIG. 2 illustrate the conditions for a pixel in the ON state and in theOFF state. Here, and in some other Figures, only one pixel is shown, butit will be appreciated by those skilled in the art that a real displaydevice may have any number of pixels, up to several million pixels ormore. It is noted that the single pixels shown in FIGS. 2 and 3 do notcomprise a scale. The length of a side of a pixel of FIG. 2 would beapproximately the same size as the diameter of the lens shown on thetight side.

FIG. 3 shows the use of an electrowetting cell in combination with aconverging or focusing element and a diffuser foil according to a secondexample of a display device. Such an arrangement is preferable if nofurther imaging is required, and if the diffuser foil is to be used asan illuminated display surface. The two sub-figures of FIG. 3 illustratethe conditions for a pixel in the ON state and one in the OFF state.Here only one pixel is shown, but it will be appreciated by thoseskilled in the art that a real display device may have any number ofpixels, up to several million pixels or more.

FIG. 4 illustrates various examples of the electrowetting cell. Theaperture of the electrowetting cell can have various forms. A preferredexample is a circular aperture, as already described above, which allowsa spherical secondary wave to be formed when the light is emittedthrough the opening. Another preferred example is a slit aperture, whichallows a cylindrical secondary wave to be formed when the light isemitted through the opening. In the latter example, the electrowettingcell has a rectangular base, where the absorbing liquid is for examplearranged in the form of a line.

According to a preferred arrangement, multiple pixels are arranged inthe form of a line array or matrix. The individual pixels are discretelycontrollable. Because of their small size, they are capable of switchingfast or very fast. An arrangement in the form of a matrix is preferredin the context of display applications. Colour contents may be presentedon the display by switching on the primary colours red, green and blueone after another using a time multiplexing method. The colour mixturemay be achieved by way of pulse width modulation, which is realisedeither in the light source, on the way to the display pixel according tothis implementation, or directly in the electrowetting cell. The latteris achieved by varying the hold time of the cell in the ON or OFF state.However, individual cells for the display of primary colours are alsopossible.

A further example according to this implementation relates to a variablelight source or to a variable light source array. The light source hastherein preferably the form of a point or line light source. The term‘variable’ is used here to describe a variable intensity of therespective source. An arrangement as sketched exemplarily in FIG. 4 canbe used to generate spherical or cylindrical secondary waves withvariable amplitude. Variable or switchable light sources are of interestfor example for applications such as in holographic displays, amplitudemodulation displays, or in optical measuring equipment.

An advantage of electrowetting cells is that the moving parts areliquid. The absence of moving solid parts reduces device wear comparedto devices in which moving solid parts are in mechanical contact withother solid parts, where device wear reduces device lifetime andconsistency of performance over time.

One skilled in the art will appreciate that amplitude modulation may beimplemented on a pixel by pixel basis, and that a display may contain upto several million pixels, or more. The amplitude spatial modulatordescribed may be used in a 3D display, such as a holographic display,especially in a holographic display in which the viewer views theholographic reconstruction through virtual observer windows. One or twovirtual observer windows for the eyes of each of one or more observersare used. The amplitude spatial modulator described may also be used ina two dimensional amplitude modulating display, or in other applicationsin which amplitude modulating spatial light modulators are employed. Theamplitude spatial modulator described may be used in transmission, or ina reflective geometry.

B. Amplitude Modulating Device for Imaging Means and HolographicDisplays

The aim is to realize fast amplitude modulating devices which can beused in 2D or 3D displays. 3D displays include holographic displays,especially holographic displays which use the applicant's preferredapproach to holography, as described for example in US2006/055994,US2006/139711, and in US2006/139710, which are incorporated byreference. A fast modulation of the pixels gives the opportunity toimplement techniques like temporally multiplexed viewing windows orcross talk reduction by sparse object reconstruction. Sparse objectreconstruction means that only a part of the grid of all object pointsis reconstructed in a given frame. Thus, the amount of cross talkbetween neighbouring object points can be reduced. For example, if onlyeach second object point in the x and the y direction is reconstructedin one frame then four frames are needed to reconstruct all objectpoints. This is one reason why faster SLM pixels are desirable. Forexample, if only the fourth object point is reconstructed, in x and ydirection respectively, then sixteen frames of this sparsereconstruction will reconstruct all object points.

The response time of the light modulating devices should be fast and thenumber of realized intensity values of reconstructed (or displayed)object points should be high enough to provide a viewer with anacceptable quality image. However, the spatial light modulator may alsobe operable at more conventional switching frequencies. The SLM may haveamplitude modulating pixels, phase modulating pixels or complex valuegenerating pixels.

One opportunity is to use a surface relief grating which acts as adiffractive lens, where a liquid crystal is used to fill the grooves ofthe surface grating structure. In an index matched situation wheren_(LC)=n_(substrate), the device will act as a plane plate i.e. a planewave will propagate through this device without any propagationdirection change. In other words, the plane wave sees no grating-likestructure in this case.

If a voltage U is applied, the refractive index of the liquid crystaln_(LC) experienced by the input light wave is changed. The electrodescan be made transparent, e.g. by using ITO. In a refractive setup, acontinuous change of the voltage will cause a continuous shift of thefocus point. In a diffractive setup, a continuous change of the voltagewill cause a continuous change of the diffraction efficiency of thegrating. Thus, the binary surface relief grating can realize a fixedfocal point with different intensity values from zero to one hundredpercent of the initial intensity. The part which is not diffracted willpass through the element as a plane wave. This non-diffracted wave isshown in FIG. 6 by the dotted lines propagating straight ahead for lightexiting the device.

In FIG. 6, a controllable refractive index n_(LC) of a liquid crystalinside a surface relief grating leads to a controllable intensity at afixed focal point. The part of the diffracted light (dashed lines forlight exiting the device in FIG. 6) depends on the diffractionefficiency η of the diffractive structure. The diffraction efficiency ischanged by the change of the modulation given byΔn(U)=n_(LC)(U)−n_(substrate). In FIG. 6, gradient discontinuities arepresent at the boundaries between the liquid crystal domains and thehost material.

If an aperture stop (AS) is placed behind a variable lens, then theintensity which propagates behind the aperture stop is controlled by thevoltage being applied. In the case of a diffractive lens the aperturestop is placed in the fixed focal plane with a distance of the focallength f to the lens, or light modulation element. This is shown in FIG.7A. To obtain a collimated plane wave, a second lens is added to thearrangement of FIG. 7A, leading to the setup shown in FIG. 7B. If theinner area of the aperture stop is too large, then a significant part ofthe non-diffracted light will still propagate behind the aperture stop.Thus the contrast which can be realized might be too low in respect tothe specific application of the modulator. This problem can be reducedby placing a spherical lens or ball lens inside the aperture stop, asshown in FIG. 7C. As shown in FIG. 7C, the light being focused by thevariable lens will pass through the small sphere without a change. Aplane wave entering the sphere will leave the sphere with a strongdivergence, as shown by the strongly diverging rays for light exitingthe spherical lens in FIG. 7C. That means that the part of the planewave which enters the transmitting area of the aperture stop will spreadout. Thus the proportion of this unwanted light is reducedsignificantly.

The benefit of using a device consisting of a surface relief gratingbeing filled with a liquid crystal is the opportunity to realize a fastswitching time of less than 5 ms, and in a preferred case less than 2ms, but still typically greater than 100 microseconds if liquid crystalsare used. For a small numerical aperture of NA<0.4 it can be assumedthat the realized functionality is independent of the polarisation ofthe light used. It is also possible to use electro-optical materials.Such materials are used for instance in Kerr cells or Pockels cells.Low-voltage crystalline materials need at least 100 V and high-voltagematerials need several thousand volts in order to switch, but theswitching time may be less than 100 microseconds.

It is also possible to use a multi order Fresnel lens instead of abinary surface relief structure. Thus the modulator can be optimized towork for several wavelengths in the same way.

It is also possible to fill a continuously shaped (i.e. no abrupt edgesare present, or equivalently, no gradient discontinuities are present)surface relief pattern with a liquid crystal. Thus, a continuous shiftof the focal point can be achieved by applying a voltage U. If the focallength f(U) is chosen to be equivalent to the distance of the aperturestop (AS), then approximately all the intensity is transmitted throughthe modulator. Only a small part of the propagating light will pass theaperture stop if the focal length is set to infinity. The part whichpropagates behind a second lens which is used to recollimate the light,analogously to FIG. 7B, can be reduced significantly. This can be doneby implementing a small spherical lens inside the centre of the aperturestop. With such a spherical lens, the setup is analogous to FIG. 7C.

One opportunity to achieve a variable focal length used for an amplitudemodulating element is to use an electro wetting cell. In this casepossible setups are equivalent to the setups shown in FIG. 7. Thediffractive lens is replaced by an electro wetting lens which realizes avariable focal length f(U). Electrowetting cells may be as discussedelsewhere in this document.

If a phase shift is realized by a variable focal length and in additionto that an aperture stop is used which is made of a light absorbingelectro wetting fluid, then an element realizing complex values of thepropagating field is obtained. If one looks at the part of the lightwhich is on axis then the change of the focal length of an electrowetting lens is equivalent to a change of the optical path length. Thusthe phase is changed if the central thickness of a lens is changed. Itis known that light absorbing oil may be used to form optical valves inflat panel displays using electro wetting. The same oil can be used fordifferent wavelengths.

There are different opportunities to enhance the contrast which can beobtained by the modulating element. One opportunity is to generate acircular focus. For instance this can be done by combining a lensfunction with a circular aperture, a Fabry-Perot interferometer or withan axicon. An axicon is a specialized type of lens which has a conicalsurface. It is also sometimes called a cone lens. An axicon transforms acollimated laser beam into Bessel beam. If in addition to that a convexlens is used, then a ring is formed. The focal distance f(U) can bechosen in a way that the complete circular spot will pass the aperturestop. This is shown in FIG. 8. By changing the focal length, the focalspot can be enlarged in a way that no propagating light will pass theaperture stop. Thus a continuous intensity range from zero to onehundred percent of the initial value can be chosen by applying theappropriate voltage.

For the case of a Fabry-Perot interferometer, if a Fabry-Perotinterferometer is illuminated with a converging spherical wave then aset of circular rings can be seen at the exit plane of the Fabry-Perotetalon. This behaviour of an etalon is well known. A change of the focallength of the lens which is placed in front of the Fabry-Perot etaloncan be used to change the diameter of a circular ring.

In FIG. 8, a circular focus can be used to obtain an amplitudemodulating device with a high contrast. By changing the focal length ofa lens the intensity value being transmitted can be chosen.

A circular spot is realized by a combination of an axicon and a lens.Also a circular phase function in front of a lens can be used to obtaina circular focus. An enlarged circular focus will be stopped by theaperture stop AS in a way that no light will pass the central clear areaof the aperture stop AS. Thus a high contrast can be obtained. A smallenough ring will be fully transmitted whereas a large ring will be fullyblocked. If inside the inner area of the aperture stop, shown in FIG. 8,a diffuser is placed, then a second lens will collimate the propagatinglight in the required way without a change of the z position of thissecond lens or without a change of the focal length of this second lens.

FIG. 9 shows the generation of a circular focus by combining a lens withan axicon. The diameter of the circular focus can be changedcontinuously by changing the focal length of the lens.

As a modification of the setup discussed so far, the diameter of thecircular spot also can be changed by implementing a variable axicon. Aliquid crystal combined with a cone can act as a variable axicon.

FIG. 10 shows a side view of a combination of a lens and an axicon whichforms a circular focus.

FIG. 11 shows a circular focus behind a combination of a lens and anaxicon. The image analysis is performed using Zemax software supplied byZEMAX Development Corporation, 3001 112th Avenue NE, Suite 202,Bellevue, Wash. 98004-8017 USA.

A reduction of elements needed to obtain a ring focus can be obtained byusing one surface of the lens to create the axicon. This is shown inFIG. 12, which was created using Zemax software. FIG. 12 shows a sideview and beam path through a combination of a lens and an axicon whichforms a circular focus. The diameter of the circular focus can bechanged continuously by changing the focal length of the lens. Theaxicon also can be realized as a diffractive circular structure. But aslong as the numerical aperture is low (e.g. NA<0.4), the functionalityof the setups discussed here is independent of the polarization state ofthe light used.

FIG. 13 shows the generation of a circular focus by combining a lenswith an axicon in a single element. In FIG. 13 a 3D layout of the setupshown in FIG. 12 is shown. The light enters the setup from the left-handside and the plane where the aperture stop is placed is the plane at theright-hand side of FIG. 13.

FIG. 14 shows a realized circular focus in the image plane of the setupshown in FIG. 13, obtained using Zemax image analysis software. FIG. 14shows a two dimensional intensity distribution in the plane where anaperture stop is placed. By changing the focal length f(U) of the lensor the prism apex angle κ(∪) of the cone forming the axicon, thediameter of the circular spot can be changed. The propagating light canbe stopped by using an aperture stop AS if the diameter of the circularfocus d(∪) is chosen to be large enough.

FIG. 15 shows a realized focus in the image plane of the setup shown inFIG. 13 in the case of an increased focal length f, obtained using Zemaximage analysis software. Compared to FIG. 14, the focal length isenlarged by thirty percent.

Another approach is to use cylindrical grooves of a substrate filledwith birefringent material. This can be done in a way that onepolarization sees an index matched situation and the perpendicularpolarization sees a cylindrical lens. At the focal distance of this lensa slit is placed. Thus the amplitude can be changed by changing thepolarization state. If a slit is used to form the aperture, then thetransmission can be changed by changing the polarization state of thelight entering the configuration described.

One skilled in the art will appreciate that amplitude modulation may beimplemented on a pixel by pixel basis, and that a display may contain upto several million pixels, or more. The amplitude spatial modulatordescribed may be used in a holographic display, especially in aholographic display in which the viewer views the holographicreconstruction through virtual observer windows. The amplitude spatialmodulator described may also be used in a two dimensional amplitudemodulating display, or in other applications in which amplitudemodulating spatial light modulators are employed.

C. Spatial Light Modulator for Modulating Light Field Phase Based onElectrowetting Cells and Display Device

This implementation relates to a spatial light modulator which comprisesan array of liquid-filled cells which can be discretely controlled withthe help of the electrowetting principle such that they modulate thephase of an incident light field. The phase is modulated independentlyin each individual pixel of the liquid cell array. A cell (pixel)comprises at least three non-mixable liquid layers with at least twovariably adjustable optical interfaces, where at least two liquidsexhibit different optical properties. In general, the two variablyadjustable optical interfaces may be parallel, or they may benon-parallel, such that a prism shape results. Taking advantage of theelectrowetting principle, the contact angle of the liquids can bemodified, thus causing a variable refraction at the variable opticalinterfaces. The variable interfaces are adjusted in a targeted mannersuch that the wave emitted by the pixel (i.e. the parallel bundle ofrays) runs parallel to the waves emitted by the other pixels. Due todifferent optical path lengths within individual cells of a pixel array,a relative phase lag can be created among the waves which aretransmitted or controlled by individual pixels.

The present implementation relates to a spatial light modulator forphase modulation of a light field, and to the manufacture of such aspatial light modulator.

Various designs of spatial light modulators (SLM) are known from theprior art under various names, and some of them are discussed elsewherein this document. The best known example is a liquid crystal (LC) basedmodulator, where a voltage-induced birefringence is used for eitherphase or amplitude modulation of a light field. Spatial light modulatorsare used in a wide range of applications which are based on opticaltechnologies and where variable or adaptive elements are required. Thefields of application of spatial light modulators range from display andprojection systems for the consumer goods sector to microscopy (opticaltweezers, phase filter, digital holographic microscopy, in-vivoimaging), beam and wave front forming using dynamic diffractive elements(laser material processing, measuring equipment, focus control) opticalmeasuring equipment (digital holography, fringe projection,Shack-Hartmann sensor) and applications in maskless lithography,ultra-fast laser pulse modulation (dispersion compensation) or interrestrial telescopes (dynamic aberration correction).

Most of the liquid-crystal-based spatial light modulators which arecommercially available today exhibit switching speeds which allowrefresh rates of 60-120 Hz to be achieved i.e the switching time isgreater than 8 ms. These switching speeds are sufficient for manyapplications. However, there are many applications which require lowerswitching times or higher refresh rates. This includes in particularapplications which involve time multiplexing methods.

An object of the present implementation is to spatially modulate thephase of a light field, where the desired phase values are alteredquickly or very quickly in contrast to LC-based SLMs. The phase φ shouldbe adjustable in a range of 0≦φ<m2π, m>1 and m being a natural numberand the refresh rates which are aimed at lie in a range of between somehundred Hertz and some kHz i.e. the response time should be less than orequal to 5 ms, but typically greater than or equal to 100 microseconds.However, the spatial light modulator may also be operable at moreconventional switching frequencies. A further object is to cover theentire range of phase values by a relative modification of the phasevalues among the individual pixels of an areal matrix.

The physical functional principle of the spatial light modulatoraccording to this implementation is based on the phase lag as a resultof variable optical path lengths within an electrowetting cell. Anelectrowetting cell comprises at least three transparent optical liquidsthrough which the light is transmitted one after another, seen in thedirection of light propagation. The optical path length within a cell ischanged with the help of variably adjustable interfaces between theimmiscible liquids.

The modulator according to this implementation is not limited to thespectral range of the visible light, but includes the near infra red andnear ultraviolet. For example, military applications in the near infrared are possible, such as in laser radar systems.

Examples of this implementation are explained in detail below and areillustrated by the accompanying drawings.

A first and preferred example (shown in FIG. 16) is based on thefunctional principle of a variable, pivoting plate with parallel sides.It is known from e.g. Malacara, D., Servin, M., and Malacara, Z.,Interferogram Analysis for Optical Testing, 2^(nd) Ed. (Taylor &Francis, New York, 2005) pages 360 to 363, that a solid plate withparallel sides which is inclined out of its vertical position causesboth a phase lag and a parallel offset of the transmitted wave. Here itis disclosed that this principle can be made use of in anelectrowetting-actuated liquid cell if it is configured appropriately.

An electrowetting liquid cell may comprise three non-mixable liquidsdisposed one after another: oil- and water-based solutions can forexample be used. The centrally disposed liquid exhibits opticalproperties (in particular a refractive index n) which differ from thoseof the two outer liquids. The two outer liquids may have an identicalrefractive index. It is known from the literature that plane interfacescan be achieved between two liquids if particular voltage differencesare applied between two opposing electrodes, as shown for example bySmith, N. R., Abeysinghe, D. C., Haus, J. W., and Heikenfeld, J. OpticsExpress 14 (2006) 6557-6563. This principle is employed here. However,in a preferred example, three liquids are used and controlled such thatthe two interfaces between the three liquids are parallel. In theinitial state, the two interfaces are parallel to the outer, fixedsubstrate interfaces (inclination angle γ=0). By applying definedvoltage differences, the optical interfaces can be inclined whilemaintaining their planarity. The inclination angle is denoted by theletter γ. Further, it is provided that the inclination angles γ₁; γ₂ ofthe two variable interfaces are identical, i.e. both interfacespreferably are parallel: γ₁=γ₂ (see FIG. 16). This way, the opticalfunctionality of a pivoting coplanar plate is realised, which, however,differs from its solid counterpart known from classic optics in that thethickness of the liquid plate here changes (it reduces) as the liquidplate is inclined. This is due to the liquid volume constancy within acell. The phase lag Δφ can be derived from the geometrical conditionsand is given by

$\begin{matrix}{{\Delta \; \varphi} = {\left( \frac{2\pi}{\lambda} \right)\left\{ {\frac{{dn}_{2}}{\cos \left\lbrack {\arcsin \left( {\frac{n_{1}}{n_{2}}\sin \; \gamma} \right)} \right\rbrack} + {v\; n_{3}\tan \; \gamma}} \right\}}} & (1)\end{matrix}$

where n_(i) is the refractive index of liquid number i (i=1, 2, or 3), γis the inclination angle, d is the plate thickness, λ is the opticalwavelength in the vacuum, and v is the lateral offset, as shown in FIG.16. The effective plate thickness of the embedded liquid is defined as

$\begin{matrix}{d = {h_{b}{\sin \left( {\frac{\pi}{4} - \gamma} \right)}}} & (2)\end{matrix}$

The lateral offset v is defined as

$\begin{matrix}{v = {d\; \sin \; {\gamma\left( {1 - \frac{n_{1}\cos \; \gamma}{\sqrt{n_{2}^{2} - {n_{1}^{2}\sin^{2}\gamma}}}} \right)}}} & (3)\end{matrix}$

FIG. 16 is a cross-sectional view of a first example of anelectrowetting cell of the spatial light modulator of thisimplementation. Three transparent optical liquids are disposed in layersin a cell, which is hermetically sealed by side walls and by transparentcover substrates. In the exemplary case, an electrically insulating ornon-polar liquid (e.g. oil-based solution) is sandwiched between twopolar, electrically conductive liquids (e.g. water-based solutions).Four electrodes are disposed on the side walls and can be addresseddiscretely. More electrodes can be disposed on the other walls beingarranged parallel to the drawing plane (not shown), These electrodes canbe controlled such that a predetermined angle between an interfacebetween two adjacent liquids and the respective sidewall can beadjusted. The predetermined angle preferably is set to about 90 degrees.The optical liquids have the refractive indices n₁; n₂; n₃, whereaccording to a preferred example n₁=n₃. FIG. 16( a) shows the initialstate of the electrowetting cell, where the voltages U_(T1); U_(T2);U_(B1); U_(B1), which are applied to the electrodes, and are chosen suchthat the water contact angles θ_(T1); θ_(T2); θ_(B1); θ_(B1), are all90° in the initial state. The side walls are coated with a thin, forexample approx. 1 μm thick, hydrophobic insulation layer. The thicknessof the hydrophobic insulation layer can range from about 50 nm to up tosome The initial thickness of the central liquid layer is denoted byh_(b). FIG. 16( b) shows the cell in an actuated state. The voltagepattern applied to the electrodes is here chosen such that the centralliquid layer is inclined by an angle γ. The water contact angles areθ_(T1)=θ_(B2) and θ_(B1)=θ_(T2). This reduces the thickness d of thecentral liquid layer, where the thickness is here measured on thesurface normal to the optical interface. The optical path length of thelight which passes through the electrowetting cell changes as a resultof the refraction at the optical interfaces. This leads to a phase lagof Δφ and to a parallel offset v.

For phase modulation, each electrowetting cell comprises at least threetransparent optical liquids which are disposed in layers in a cell,which is hermetically sealed by side walls and by transparent coversubstrates, where an electrically insulating or non-polar liquid issandwiched between two polar, electrically conductive liquids, theoptical liquids having the refractive indices n₁; n₂; n₃, where fourelectrodes are disposed on the side walls and can be addresseddiscretely, and where the side walls are coated with a hydrophobicinsulation layer. The optical path length of the light which passesthrough the electrowetting cell changes as a result of the refraction atthe optical interfaces. Alternatively, the cell may comprise a layer ofpolar, electrically conductive liquid which is sandwiched between twoelectrically insulating or non-polar liquids.

FIG. 17 is a cross-sectional view of a second example of anelectrowetting cell of the spatial light modulator according to thisimplementation, which permits a controllable phase change for negligiblechange in the beam propagation direction. The general arrangement issimilar to that of the first example shown in FIG. 16; however, theelectrical addressing and thus the optical functionality of the cell aredifferent. The optical functionality of a prism is achieved with thehelp of three liquids which have the refractive indices n₁; n₂; n₃. Itis not necessary that n₁=n₃; it is also possible to use differentliquids for liquids 1 and 3. Different liquids 1 and 3 may be able tocorrect to some extent for each other's dispersion properties, andcorrect to some extent for the dispersion properties of liquid 2, forexample. The general idea is that the same deflection angles β can berealised with different combinations of prism angles γ₁; γ₂. As a resultof the refraction at the optical interface, the light passes through theelectrowetting cell on different paths and is thus given a differentphase lag than an adjacent cell with differently set prism angles γ₁;γ₂, while the deflection angle β remains the same. FIG. 17( a) shows thecell in its initial state and FIG. 17( b) shows the cell in its actuatedstate. Generally, any state can be referred to as the initial state:this term is only used to denote a reference state to which the phasevalues of other states are related.

FIG. 18 is a cross-sectional view of a preferred example of anelectrowetting cell with the objective of reducing the volume of theliquid to be moved when switching occurs, and reducing the distance theliquid has to move when switching occurs. A reduced volume of liquid tobe moved, and a reduced distance to be moved, will reduce the switchingtime. This idea can be realised in both types of cells above, i.e. thoseaccording to the first example (FIG. 16) and those according to thesecond example (FIG. 17). Two sub-cells are disposed one after another,thus representing a phase-lagging pixel of a spatial light modulator. Anoptically transparent separating substrate is sandwiched between the twosub-cells in the centre of the cell. The separating substrate canpreferably be index-matched to the refractive index of the surroundingliquid, so that there will be no loss of light caused by reflections. Inthe example according to FIG. 16, two liquids which differ in theiroptical properties are used, and in the example according to FIG. 17, atleast two different liquids are used. The optical axes of the twosub-cells do not have to coincide, and preferably they exhibit aconstant lateral offset. This constant lateral offset is preferred inorder to reduce the dynamic part of the lateral shift, which would occurin the solution according to FIG. 16, in particular if the inclinedplane plate is operated in a higher order for phase modulation. Anexample of a higher order for phase modulation is shown in FIG. 21C,where a phase shift between 0 and 2π can be achieved for values of γbetween about 25 degrees and 34 degrees. What this means is that(referring to FIG. 21A), when the apex angle γ varies from 0° to 25°, alateral shift from 0 to 10 microns will occur. On the other hand, if theapex angle varies from 25° to 34°, the lateral shift is in between 10and 14 microns. In this case, it is preferred to choose a constantlateral offset (due to laterally shifted assembly of both cells, like adecentering) of say 12 microns. Then, the variable part of the lateralshift is reduced to plus/minus 2 microns.

In FIG. 18, and indeed more generally, what is desired is the ability toproduce a phase shift between zero and 2π radians, and to achieve thisby introducing a change to the tilt of the interface between two liquidlayers which is relatively small, because the smaller the change in thetilt angle required to achieve a given phase shift, the faster the phasemodulator should be. If the liquid interface, or a plane parallel plate,is tilted to start with (i.e. if there is a shifted lateral offset),then the additional tilt which has to be introduced to obtain the neededphase shift of up to 2π is smaller or much smaller than in the case of anon tilted initial state. That is why a pre tilted liquid cell ispreferred. But if we have this large tilt in the initial state, we alsohave a large lateral shift in the beam propagation direction for anormally incident beam in the initial state of the device, because planewaves propagating normal to the cell will be propagating off-normal tothe interfaces between the liquids and hence will experience refraction.For instance this lateral offset (i.e. the lateral deflection of a beampropagating normal to the cell, when traversing the cell), defining thezero position or initial state of the cell, may be 20 percent of thewidth of a cell, it is calculated. To correct for this, we arrange thesecond array of cells (of which the cell on the right hand side of FIG.18 is an example) to compensate for the lateral offset of 20 percent ofthe width of a single cell. There is still a lateral offset v(γ) independence on the introduced phase shift, and vice versa, but thedynamic range of the variable lateral shift is greatly reduced.

FIG. 19 shows an example where the fixed prism angle β, which occurswhen realising the example shown in FIG. 17, is compensated for with thehelp of a fixed prism on the beam exit side of the device.Alternatively, the fixed prism may be on the beam entrance side of thedevice, as would be appreciated by one skilled in the art.

FIG. 20 shows an example which may be used to counteract the paralleloffset of the beam, which occurs when realising the example shown inFIG. 17. In FIG. 20, light propagates from left to right. An aperture isdisposed in a central position on the exit surface of the pixel, wheresaid aperture is designed such that it is always completely illuminated.A part of the parallel-offset light wave is absorbed by the aperture.The exit surface of a pixel thus remains localised at the position ofthe aperture and is independent of the liquid interface inclinationangle.

FIGS. 21A, B and C show the lateral beam offset or lateral shift of thebeam, the optical path length difference and the phase lag,respectively, as a function of γ, calculated for the example shown inFIG. 16. Parameters used are: n₁=n₃=1.33; n₂=1.6, h_(b)=130 μm. In orderto achieve a phase lag of 2π, several inclination regimes are possible.For example, a 2π phase lag is achieved by an inclination within therange of 0°≦γ≦25° or within the range of 25°≦γ≦34°. Because of the morefavourable linearity and a smaller variable parallel offset, it ispreferred to use a higher order, i.e. to define the initial state at avalue of γ which is different from zero, such as in the range 25°≦γ≦34°.The initial offset of the plane parallel shift can be compensated for byan equivalent but opposite plane parallel shift of the second sub-cellin respect to the first sub-cell, or by using an inclined cylindricalcavity which is filled with the liquids.

One skilled in the art will appreciate that phase modulation may beimplemented on a pixel by pixel basis, and that a display may contain upto several million pixels, or more. The phase spatial modulatordescribed may be used in a holographic display, especially in aholographic display in which the viewer views the holographicreconstruction through virtual observer windows. The phase spatialmodulator described may also be used in a two dimensional phasemodulating display, or in other applications in which phase modulatingspatial light modulators are employed.

D. Complex Spatial Light Modulator and Display Device UsingElectrowetting Cells and Display Device

The spatial light modulators of parts A and C above may be combined toprovide a complex spatial light modulator using electrowetting cells,which may be used in a display device. For complex modulation of a lightwave, it is necessary to be able to modulate the amplitude and phase ofa light wave independently. By using the spatial light modulators ofparts A and C above in series, which respectively modulate the amplitudeand the phase of a light wave, complex modulation of the light wave isenabled. The spatial light modulators of parts A and C above must beplaced in sufficient proximity that cross-talk between pixels is zero oris kept to acceptable levels i.e. display artifacts which result areacceptably small for the viewer or viewers. The refresh rates which areaimed at lie in a range of between some hundred Hertz and some kHz i.e.the response time should be less than or equal to 5 ms, but typicallygreater than or equal to 100 microseconds. However, the spatial lightmodulator may also be operable at more conventional switchingfrequencies.

The modulator according to this implementation is thus not limited tothe spectral range of the visible light, but includes the near infra redand near ultraviolet. For example, military applications in the nearinfra red are possible, such as in laser radar systems.

FIG. 22 shows a schematic representation of an optical arrangement of apreferred embodiment of the present invention, wherein amplitude andphase modulation is sequentially applied. From the left to the right—inthe direction of the propagation of the light—the following opticalcomponents are shown: a pinhole, a macro lens and a first and a secondsandwich. The pinhole denotes a primary or secondary light source. Thelight source can be of a point-like or of a line-like shape. The macrolens comprises a spherical or a cylindrical shape, collimating the lightemitted by the light source. The diameter or the cross sectional size ofthe macro lens can be in the range of several mm, for example 3 to 10mm. The first sandwich comprises micro lenses on both surfacesperpendicular to the optical axis. The diameter or the cross sectionalsize of the micro lenses can be 20 to 100 μm, for example. The microlenses comprise a spherical or a cylindrical shape. A micro lens of theleft surface of the first sandwich as shown in FIG. 22 focuses thecollimated light into an electrowetting cell. Such an electrowettingcell is comparable to an electrowetting cell as shown in FIGS. 1 to 3,i.e. it comprises a pinhole or a slit. The first sandwich comprises aplurality of such electrowetting cells being arranged next to each otherin one or more directions forming a line type or a matrix typearrangement (below each other in the representation of FIG. 22, notshown). The first sandwich is operable such that it realises a SLMmodulating the amplitude of the light directed towards the firstsandwich. The light passing through the electrowetting cell—depending onits switching state being comparable to the ones shown in FIG. 1 a toFIG. 1 c—is collimated by the micro lens of the right surface of thefirst sandwich as shown in FIG. 22. The first sandwich can be spacedapart from the second sandwich by spacers (not shown) or the firstsandwich can be in direct contact with the second sandwich. The order ofthe two sandwiches can be inverted. The second sandwich comprises aplurality of electrowetting cells being arranged next to each other inone or more directions forming a line type or a matrix type arrangement(below each other in the representation of FIG. 22, not shown). Lightcoming from an electrowetting cell of the first sandwich passes throughan electrowetting cell of the second sandwich. The electrowetting cellsof the second sandwich are of the type as shown in FIG. 18. Theelectrowetting cells of the second sandwich are operable such that theyrealises a SLM modulating the phase of the light directed through thesecond sandwich. The optical arrangement as shown in FIG. 22 can be seenas a cut-out of a display extending in vertical direction of FIG. 22 andtherefore comprising more pinholes/light sources and more macro lenses,respectively. The light emitted by the pixels of this display can bemodulated by the first and second sandwich in amplitude and/or in phaseand thus can provide complex values. Such a display can be used as ahologram bearing medium of a holographic display into which a hologramis encoded in order to visualize a holographic representation of athree-dimensional scene. Such a holographic display is described forexample in Appendix I. If light being emitted by the pixels of thedisplay needs to be deflected, e.g. in order to realize eye tracking, anadditional optical layer or sandwich can be added on the right hand sideof the second sandwich (not shown in FIG. 22).

FIG. 23 shows a schematic representation of a part of an opticalarrangement of a preferred embodiment of the present invention, whereina light source array can be provided. The single light sources of thelight source array comprise variable/adjustable phase values. Collimatedlight coming from the left side passes through an electrowetting cellbeing adapted to modulate or alter the phase of the light passingthrough the electrowetting cell. The electrowetting cell is of the typeas shown e.g. in FIGS. 16 to 20. The transmitted and still collimatedlight is focused by the spherical or cylindrical shaped lens into apinhole or into a slit, respectively. The pinhole or slit light can beregarded as a single point or as a line light source—if light is passingthrough the pinhole or slit—whose phase can be altered depending on thecontrol of the electrowetting cell. The optical arrangement as shown inFIG. 23 can be seen as a cut-out of an array of a plurality of lightsources, electrowetting cells, lenses and pinholes being arranged invertical direction of FIG. 23. The phase values of the light sources ofthis array can be modulated independently from each other.

FIG. 24 shows a schematic representation of a part of another opticalarrangement of a preferred embodiment of the present invention, whereina light source array can be provided. The single light sources of thelight source array comprise variable/adjustable phase and amplitudevalues. Collimated light coming from the left side passes through anelectrowetting cell being adapted to modulate or alter the phase of thelight passing through the electrowetting cell. The electrowetting cellis of the type as shown e.g. in FIGS. 16 to 20. The transmitted andstill collimated light is focused by the spherical or cylindrical shapedlens into a second electrowetting cell comprising a pinhole or a slit,respectively. The second electrowetting cell can be one as shown inFIGS. 1 to 3. Therefore, the second electrowetting cell is adapted tomodulate the amplitude of the light passing it in dependence of itsswitching state. The pinhole or slit of the second electrowetting cellcan be regarded as a single point or line light source—if light ispassing through the pinhole or slit—whose phase and/or amplitude can bealtered depending on the control of the two electrowetting cells. Theoptical arrangement as shown in FIG. 24 can be seen as a cut-out of anarray of a plurality of light sources, electrowetting cells and lensesbeing arranged in vertical direction of FIG. 24. The phase and/oramplitude values of the light sources of this array can be modulatedindependently from each other.

One skilled in the art will appreciate that complex modulation may beimplemented on a pixel by pixel basis, and that a display may contain upto several million pixels, or more. The complex spatial modulatordescribed may be used in a holographic display, especially in aholographic display in which the viewer views the holographicreconstruction through one or two virtual observer windows. The complexspatial modulator described may also be used in other applications, aswould be obvious to one skilled in the art.

Notes

While the implementations have been illustrated and described in detailby the foregoing description in conjunction with the accompanyingdrawings, such illustration and description shall be consideredillustrative and exemplary and not restrictive. The implementationsshall not be limited to the disclosed examples. Other variations in thedisclosed examples can be understood and effected by those skilled inthe art in practicing the implementations, from a study of the drawingsand the disclosure.

In the Figures herein, the relative dimensions shown are not necessarilyto scale.

Various modifications and alterations of this invention will becomeapparent to those skilled in the art without departing from the scope ofthis invention, and it should be understood that this invention is notto be unduly limited to the illustrative examples and implementationsset forth herein.

APPENDIX I

Technical Primer

The following section is meant as a primer to several key techniquesused in some of the systems that implement the present invention.

In conventional holography, the observer can see a holographicreconstruction of an object (which could be a changing scene); hisdistance from the hologram is not however relevant. The reconstructionis, in one typical optical arrangement, at or near the image plane ofthe light source illuminating the hologram and hence is at the Fourierplane of the hologram. Therefore, the reconstruction has the samefar-field light distribution of the real world object that isreconstructed.

One early system (described in WO 2004/044659 and US 2006/0055994)defines a very different arrangement in which the reconstructed objectis not at or near the Fourier plane of the hologram at all. Instead, avirtual observer window zone is at the Fourier plane of the hologram;the observer positions his eyes at this location and only then can acorrect reconstruction be seen. The hologram is encoded on a LCD (orother kind of spatial light modulator) and illuminated so that thevirtual observer window becomes the Fourier transform of the hologram(hence it is a Fourier transform that is imaged directly onto the eyes);the reconstructed object is then the Fresnel transform of the hologramsince it is not in the focus plane of the lens. It is instead defined bya near-field light distribution (modeled using spherical wavefronts, asopposed to the planar wavefronts of a far field distribution). Thisreconstruction can appear anywhere between the virtual observer window(which is, as noted above, in the Fourier plane of the hologram) and theLCD or even behind the LCD as a virtual object.

There are several consequences to this approach. First, the fundamentallimitation facing designers of holographic video systems is the pixelpitch of the LCD (or other kind of light modulator). The goal is toenable large holographic reconstructions using LCDs with pixel pitchesthat are commercially available at reasonable cost. But in the past thishas been impossible for the following reason. The periodicity intervalbetween adjacent diffraction orders in the Fourier plane is given byλD/p, where λ is the wavelength of the illuminating light, D is thedistance from the hologram to the Fourier plane and p is the pixel pitchof the LCD. But in conventional holographic displays, the reconstructedobject is in the Fourier plane. Hence, a reconstructed object has to bekept smaller than the periodicity interval; if it were larger, then itsedges would blur into a reconstruction from an adjacent diffractionorder. This leads to very small reconstructed objects—typically just afew cm across, even with costly, specialised small pitch displays. Butwith the present approach, the virtual observer window (which is, asnoted above, positioned to be in the Fourier plane of the hologram) needonly be as large as the eye pupil. As a consequence, even LCDs with amoderate pitch size can be used. And because the reconstructed objectcan entirely fill the frustum between the virtual observer window andthe hologram, it can be very large indeed, i.e. much larger than theperiodicity interval. Further, where an OASLM is used, then there is nopixelation, and hence no periodicity, so that the constraint of keepingthe virtual observer window smaller than a periodicity interval nolonger applies.

There is another advantage as well, deployed in one variant. Whencomputing a hologram, one starts with one's knowledge of thereconstructed object—e.g. you might have a 3D image file of a racingcar. That file will describe how the object should be seen from a numberof different viewing positions. In conventional holography, the hologramneeded to generate a reconstruction of the racing car is deriveddirectly from the 3D image file in a computationally intensive process.But the virtual observer window approach enables a different and morecomputationally efficient technique. Starting with one plane of thereconstructed object, we can compute the virtual observer window as thisis the Fresnel transform of the object. We then perform this for allobject planes, summing the results to produce a cumulative Fresneltransform; this defines the wave field across the virtual observerwindow. We then compute the hologram as the Fourier transform of thisvirtual observer window. As the virtual observer window contains all theinformation of the object, only the single-plane virtual observer windowhas to be transformed to the hologram and not the multi-plane object.This is particularly advantageous if there is not a singletransformation step from the virtual observer window to the hologram butan iterative transformation like the Iterative Fourier TransformationAlgorithm. Each iteration step comprises only a single Fouriertransformation of the virtual observer window instead of one for eachobject plane, resulting in significantly reduced computation effort.

Another interesting consequence of the virtual observer window approachis that all the information needed to reconstruct a given object pointis contained within a relatively small section of the hologram; thiscontrasts with conventional holograms in which information toreconstruct a given object point is distributed across the entirehologram. Because we need encode information into a substantiallysmaller section of the hologram, that means that the amount ofinformation we need to process and encode is far lower than for aconventional hologram. That in turn means that conventionalcomputational devices (e.g. a conventional digital signal processor(DSP) with cost and performance suitable for a mass market device) canbe used even for real time video holography.

There are some less than desirable consequences however. First, theviewing distance from the hologram is important—the hologram is encodedand illuminated in such a way that only when the eyes are positioned atthe Fourier plane of the hologram is the optimal reconstruction seen;whereas in normal holograms, the viewing distance is not important.There are however various techniques for reducing this Z sensitivity ordesigning around it, and in practice the Z sensitivity of theholographic reconstruction is usually not extreme.

Also, because the hologram is encoded and illuminated in such a way thatoptimal holographic reconstructions can only be seen from a precise andsmall viewing position (i.e. precisely defined Z, as noted above, butalso X and Y co-ordinates), eye tracking may be needed. As with Zsensitivity, various techniques for reducing the X, Y sensitivity ordesigning around it exist. For example, as pixel pitch decreases (as itwill with LCD manufacturing advances), the virtual observer window sizewill increase. Furthermore, more efficient encoding techniques (likeKinoform encoding) facilitate the use of a larger part of theperiodicity interval as virtual observer window and hence the increaseof the virtual observer window.

The above description has assumed that we are dealing with Fourierholograms. The virtual observer window is in the Fourier plane of thehologram, i.e. in the image plane of the light source. As an advantage,the undiffracted light is focused in the so-called DC-spot. Thetechnique can also be used for Fresnel holograms where the virtualobserver window is not in the image plane of the light source. However,care must be taken that the undiffracted light is not visible as adisturbing background. Another point to note is that the term transformshould be construed to include any mathematical or computationaltechnique that is equivalent to or approximates to a transform thatdescribes the propagation of light. Transforms are merely approximationsto physical processes more accurately defined by Maxwellian wavepropagation equations; Fresnel and Fourier transforms are second orderapproximations, but have the advantages that (a) because they arealgebraic as opposed to differential, they can be handled in acomputationally efficient manner and (ii) can be accurately implementedin optical systems.

Further details are given in US patent application 2006-0138711, US2006-0139710 and US 2006-0250671, the contents of which are incorporatedby reference.

APPENDIX II Glossary of Terms Used in the Description

Computer Generated Hologram

A computer generated video hologram CGH is a hologram that is calculatedfrom a scene. The CGH may comprise complex-valued numbers representingthe amplitude and phase of light waves that are needed to reconstructthe scene. The CGH may be calculated e.g. by coherent ray tracing, bysimulating the interference between the scene and a reference wave, orby Fourier or Fresnel trans form.

Encoding

Encoding is the procedure in which a spatial light modulator (e.g. itsconstituent cells, or contiguous regions for a continuous SLM like anOASLM) are supplied with control values of the video hologram. Ingeneral, a hologram comprises of complex-valued numbers representingamplitude and phase.

Encoded Area

The encoded area is typically a spatially limited area of the videohologram where the hologram information of a single scene point isencoded. The spatial limitation may either be realized by an abrupttruncation or by a smooth transition achieved by Fourier transform of avirtual observer window to the video hologram.

Fourier Transform

The Fourier transform is used to calculate the propagation of light inthe far field of the spatial light modulator. The wave front isdescribed by plane waves.

Fourier Plane

The Fourier plane contains the Fourier transform of the lightdistribution at the spatial light modulator. Without any focusing lensthe Fourier plane is at infinity. The Fourier plane is equal to theplane containing the image of the light source if a focusing lens is inthe light path close to the spatial light modulator.

Fresnel Transform

The Fresnel transform is used to calculate the propagation of light inthe near field of the spatial light modulator. The wave front isdescribed by spherical waves. The phase factor of the light wavecomprises a term that depends quadratically on the lateral coordinate.

Frustum

A virtual frustum is constructed between a virtual observer window andthe SLM and is extended behind the SLM. The scene is reconstructedinside this frustum. The size of the reconstructed scene is limited bythis frustum and not by the periodicity interval of the SLM.

Imaging Optics

Imaging optics are one or more optical components such as a lens, alenticular array, or a microlens array used to form an image of a lightsource (or light sources). References herein to an absence of imagingoptics imply that no imaging optics are used to form an image of the oneor two SLMs as described herein at a plane situated between the Fourierplane and the one or two SLMs, in constructing the holographicreconstruction.

Light System

The light system may include either of a coherent light source like alaser or a partially coherent light source like a LED. The temporal andspatial coherence of the partially coherent light source has to besufficient to facilitate a good scene reconstruction, i.e. the spectralline width and the lateral extension of the emitting surface have to besufficiently small.

Virtual Observer Window (VOW)

The virtual observer window is a virtual window in the observer planethrough which the reconstructed 3D object can be seen. The VOW is theFourier transform of the hologram and is positioned within oneperiodicity interval in order to avoid multiple reconstructions of theobject being visible. The size of the VOW has to be at least the size ofan eye pupil. The VOW may be much smaller than the lateral range ofobserver movement if at least one VOW is positioned at the observer'seyes with an observer tracking system. This facilitates the use of a SLMwith moderate resolution and hence small periodicity interval. The VOWcan be imagined as a keyhole through which the reconstructed 3D objectcan be seen, either one VOW for each eye or one VOW for both eyestogether.

Periodicity Interval

The CGH is sampled if it is displayed on a SLM composed of individuallyaddressable cells. This sampling leads to a periodic repetition of thediffraction pattern. The periodicity interval is λD/p, where λ is thewavelength, D the distance from the hologram to the Fourier plane, and pthe pitch of the SLM cells. OASLMs however have no sampling and hencethere is no periodic repetition of the diffraction pattern; therepetitions are in effect suppressed.

Reconstruction

The illuminated spatial light modulator encoded with the hologramreconstructs the original light distribution. This light distributionwas used to calculate the hologram. Ideally, the observer would not beable to distinguish the reconstructed light distribution from theoriginal light distribution. In most holographic displays the lightdistribution of the scene is reconstructed. In our display, rather thelight distribution in the virtual observer window is reconstructed.

Scene

The scene that is to be reconstructed is a real or computer generatedthree-dimensional light distribution. As a special case, it may also bea two-dimensional light distribution. A scene can constitute differentfixed or moving objects arranged in a space.

Spatial Light Modulator (SLM)

A SLM is used to modulate the wave front of the incoming light. An idealSLM would be capable of representing arbitrary complex-valued numbers,i.e. of separately controlling the amplitude and the phase of a lightwave. However, a typical conventional SLM controls only one property,either amplitude or phase, with the undesirable side effect of alsoaffecting the other property.

1. A spatial light modulator comprising pixels, where for each pixel, alight field amplitude transmitted by the pixel is modulated by anelectrowetting cell, wherein the electrowetting cell is illuminated withconverging light comprising a focus, the convergent light is generatedby a focusing element, wherein an electrowetting cell comprises a coversubstrate with a top face, the top face being coated with an opticallynon-transparent layer, which exhibits a centrally disposed opticallytransmitting aperture, the aperture effecting a spatial filtering andwherein the electrowetting cell is disposed near the focus of the lightsuch that the position of the aperture of the electrowetting cellcoincides with the position of the focus of the light.
 2. The spatiallight modulator of claim 1, especially for modulating the light fieldamplitude, in which each electrowetting cell comprises a firstsubstantially transparent substrate coated with a substantiallytransparent electrode and a hydrophobic isolation layer, apixel-separating side wall, at least two immiscible liquids, one of theliquids being opaque or absorbing and one of the liquids beingelectrically conductive or polar liquid, and a second, substantiallytransparent substrate and where the amount of light passing through theelectrowetting cell is controlled by a voltage applied to theelectrically conductive or polar liquid.
 3. The spatial light modulatorof claim 1, especially for modulating the light field amplitude, inwhich each electrowetting cell comprises a first substantiallytransparent substrate coated with a substantially transparent electrodeand hydrophobic isolation layers, a pixel-separating side wall, a firstopaque or absorbing liquid and a second electrically conductive or polarliquid where these two liquids are immiscible, and a second,substantially transparent substrate and where the amount of lightpassing through the electrowetting cell is controlled by a voltageapplied to the electrically conductive or polar liquid.
 4. The spatiallight modulator of claim 2 or 3, in which a contact angle of theelectrically conductive or polar liquid and the first substantiallytransparent substrate is continuously variable by applying differentvoltages thus realising a continuously variable absorption in the cell.5. The spatial light modulator of claims 2 or 3, in which the top faceof the second substrate is coated with an optically non-transparent,layer, which exhibits an essentially centrally disposed opticallytransmitting opening.
 6. The spatial light modulator of claims 2 or 3,in which the electrowetting cell is in the ON state if a DC or ACvoltage is applied between an electrode and a counter electrode, wherebythe electrically conductive or polar liquid is attracted to thehydrophobic insulator layer caused by electrostatic forces, therebydisplacing the opaque or absorbing liquid, which is positioned around acentral spot on the first substantially transparent substrate, and thecell is in its OFF state if no voltage is applied.
 7. The spatial lightmodulator of claims 2 or 3, in which the opaque or absorbing liquid isdisposed at fringes of the electrowetting cell and is held in thisposition by suitable means such that if no voltage is applied, theopaque or absorbing liquid spreads across the base area; a smallseparation ring is positioned in the centre of the cell, which ensuresthat there is permanent contact to the electrically conductive or polarliquid and that the opaque or absorbing liquid spreads homogeneously inall directions when the cell is switched on.
 8. A spatial lightmodulator comprising pixels, where for each pixel, a light field phasetransmitted by the pixel is modulated by an electrowetting cell, inwhich each electrowetting cell comprises at least three non-mixableliquid layers with at least two variably adjustable optical interfaces,wherein at least two liquids exhibit different optical properties,wherein the phase of an incident light field is modulated independentlyin each individual pixel of the spatial light modulator, wherein the atleast two variably adjustable optical interfaces are adjusted in atargeted manner such that a relative phase lag is created among thelight waves which are controlled by individual pixels due to differentoptical path lengths within individual electrowetting cells of thespatial light modulator.
 9. The spatial light modulator of claim 8, inwhich the liquid layer in the middle of the three liquid layers forms aninclined, essentially plane plate which is operated in a higher orderfor phase modulation or in which the liquid layer in the middle of thethree liquid layers forms an inclined, essentially plane plate which isoperated in a higher order for phase modulation and in which the liquidlayer in the middle of the three liquid layers forms an inclined,essentially plane plate, and a second electrowetting cell is placedafter the first cell to compensate for lateral offset of light beamstransmitting the first electrowetting cell. 10-11. (canceled)
 12. Thespatial light modulator of claim 9, in which the liquid layer in themiddle of the three liquid layers forms an inclined, essentially planeplate, and a fixed prism is placed on the beam entrance side or on abeam exit side of the electrowetting cell to compensate for lateraloffset of light beams transmitting the electrowetting cell.
 13. Thespatial light modulator of claim 9, in which the liquid layer in themiddle of the three liquid layers forms an inclined plane plate, and anaperture is disposed in a central position on a beam exit side of theelectrowetting cell to prevent lateral offset of light beamstransmitting the electrowetting cell.
 14. A spatial light modulatorcomprising pixels, where for each pixel, the light field is modulated ona complex number basis using two electrowetting cells in series for eachpixel, one of the two electrowetting cells being an electrowetting cellaccording to claim 1 and/or one of the electrowetting cell being anelectrowetting cell according to claim 8, the two electrowetting cellspermitting independent modulation of amplitude and phase of the complexnumber.
 15. The spatial light modulator of claim 14, in which the twocells are located in sufficient proximity that cross-talk between pixelsis zero or is kept to acceptable levels.
 16. The spatial light modulatorof claim 1, 8 or 14, in which multiple pixels are arranged in the formof a line array or matrix.
 17. The spatial light modulator of claim 1, 8or 14, in which the light field amplitude transmitted by each pixel ismodulated with a switching time less than or equal to 5 ms and/orgreater than or equal to 100 microseconds.
 18. The spatial lightmodulator of claim 17, in which the spatial light modulator is operableat conventional switching frequencies, preferably in the frequency rangefrom 15 Hz to several KHz, or in which the spatial light modulator isoperable to maintain a predetermined state for a predetermined period oftime.
 19. The spatial light modulator of claim 1, 8 or 14, in which theelectrowetting cell is positioned near a focus of a focusing element orin which the electrowetting cell is positioned near a focus of afocusing element and in which the size of the electrowetting cell issmaller or much smaller than the size of the focusing element. 20.(canceled)
 21. The spatial light modulator of claim 1, 8 or 14, in whichthe light transmitted through the electrowetting cell is transmittedwith a spherical or cylindrical outgoing wavefront, due to at least onelight beam forming means being assigned to the electrowetting cell.22-23. (canceled)
 24. The spatial light modulator of claim 1, 8 or 14,in which the spatial light modulator is used to form a secondary lightsource or in which the spatial light modulator is used to form a lightsource array with variable amplitude or in which the spatial lightmodulator is used to form a light source array with variable phase.25-26. (canceled)
 27. The spatial light modulator of claim 1, 8 or 14,in which the spatial light modulator is used in transmission or in areflective geometry.
 28. (canceled)
 29. The spatial light modulator ofclaim 1, 8 or 14, in which the spatial light modulator is used in a 3Ddisplay or in a holographic display or in a stereoscopic display or in atwo dimensional amplitude modulating display or in which the spatiallight modulator is used in a holographic display and in which one or twovirtual observer windows for the eyes of one or more observers are used.30-32. (canceled)
 33. Device or display device including the spatiallight modulator of claim 1, 8 or 14, in which the device is a phaseand/or an amplitude modulating device or in which the device is acomplex light wave modulating device. 34-36. (canceled)
 37. The displaydevice of claim 33, in which the display device is a 2D phase modulatingdisplay device or a stereoscopic display device or in which the displaydevice is a holographic display device and in which the holographicdisplay device preferably uses virtual observer windows for the eyes ofthe observer or observers.
 38. (canceled)
 39. Method of using a displaydevice of claim 33, the display including a light source and an opticalsystem to illuminate the spatial light modulator; comprising the stepof: for each pixel, modulating the light field amplitude transmitted byeach pixel using an electrowetting cell and/or modulating the lightfield phase transmitted by each pixel using an electrowetting cell.